Answer:
176/1125 or 0.156
Step-by-step explanation:
There are 15 bulbs, of which 4 are 23-watt. The probability of selecting a 23-watt bulb = 4/15. If we call this probability x, then x = 4/15.
The probability of selecting a 13-watt or 18-watt bulb is the probability of not selecting a 23-watt bulb. If we call this y, y = (6+5)/15 = 11/15. It follows that x and y are mutually exclusive. Here, we have a binomial distribution.
The number of ways of selecting exactly two 23-watt bulbs out of three is
[tex]\binom{3}{2} = 3[/tex]
The probability of selecting them is
[tex]3x^2y = 3\times\left(\dfrac{4}{15}\right)^2\times\dfrac{11}{15}=\dfrac{176}{1125}= 0.156[/tex]
